Optimal burst transmission times through single modems

ABSTRACT

The present disclosure generally relates to systems, methods and software for determining an optimal burst transmission time through a modem, such as a cable modem, a wireless access point, a node in a cable network, or a satellite communication link. Particularly, the present disclosure makes it possible for a burst of queued data, defined as data above a certain percentile of a monitored traffic rate, to be transmitted by the modem at a time that provides the best chance of avoiding a collision with a co-occurring burst of data from another user connected to the same modem. In an embodiment, the systems, methods and software disclosed herein use the optimal transmission time to replace a contention window transmission time, at least for bursty data, or they completely eliminate the need for contention windows, at least for bursty data.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation of U.S. patent application Ser. No.16/659,771, filed Oct. 22, 2019, which application claims the benefit ofand priority to U.S. Provisional Patent Application No. 62/748,836,filed Oct. 22, 2018, which is hereby incorporated by reference in itsentirety.

STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH

None.

BACKGROUND

Digital content has become increasingly bandwidth intensive and subjectto intermittent, high-volume spikes. For example, when an Internet userswitches between written content and video content, online gaming, oranother streaming activity, data consumption rises. Such spikes place ahigh burden on data hubs, nodes and modems, where high-volume demandsfrom multiple users at random intervals merge and can lead to datacollisions and failed transmissions.

SUMMARY

The present disclosure generally relates to systems, methods andsoftware for determining an optimal burst transmission time through amodem, such as a cable modem, a wireless access point, a node in a cablenetwork, or a satellite communication link. Particularly, the presentdisclosure makes it possible for a burst of queued data, defined as dataabove a certain percentile of a monitored traffic rate, to betransmitted by the modem at a time that provides the best chance ofavoiding a collision with a co-occurring burst of data from another userconnected to the same modem. In an embodiment, the systems, methods andsoftware disclosed herein use the optimal transmission time to replace acontention window transmission time, at least for bursty data, or theycompletely eliminate the need for contention windows, at least forbursty data.

In an aspect, a method for determining an optimal burst transmissiontime through a modem comprises: monitoring a traffic rate through amodem over a period; identifying a burst in the traffic rate when thetraffic rate exceeds a threshold; measuring inter-burst gaps, where thegaps are defined by a minimum time passage and a maximum time passage;determining a mean and a standard deviation of a lognormal distributionof the inter-burst gaps; using the mean and the standard deviation ofthe lognormal distribution in a moment-generating function to identifyan average time passage value when the risk of a co-occurring burst isminimized; and inserting the average time passage value as a mean in themoment-generating function to back-calculate an optimal transmissiontime for a queued burst of traffic.

In an embodiment, a method for determining an optimal burst transmissiontime through a modem further comprises instructing the modem to transmitthe queued burst of traffic at the optimal transmission time.

In an embodiment, a method for determining an optimal burst transmissiontime through a modem further comprises periodically updating the optimaltransmission time by repeating the steps of monitoring, identifying,measuring, determining, using, inserting and instructing.

In an embodiment, a method for determining an optimal burst transmissiontime through a modem further comprises scaling the traffic rate.

In an embodiment, the threshold is set at the 80^(th), 85^(th), 90^(th),92^(nd), 95^(th), 97^(th), 98^(th), or 99^(th) percentile.

The minimum time passage for an inter-burst gap may be set at a smallvalue to better distinguish between neighboring bursts that occur closein time, for example, to detect more bursts and increase burst frequencystatistics, while a maximum time passage for an inter-burst gap may beset at a value that would accommodate the largest anticipated burst. Inan embodiment, the minimum time passage for an inter-burst gap is 11seconds and the maximum time passage for an inter-burst gap is 200seconds.

In an embodiment, the optimal transmission time replaces a contentionwindow transmission time, at least for bursty data, or completelyeliminates the need for a contention window.

In an embodiment, the optimal transmission time is periodically updatedat least one per year, quarter, month, week, day or hour.

In an embodiment, the optimal transmission time is based on a continuoustimer that is independent of any trigger or start/stop phenomenon. Forexample, a continuous timer may be based on Greenwich Mean Time. In anembodiment, the optimal transmission time is a count within a contentionwindow.

In an embodiment, the modem is a single modem, a wireless access point,a node in a cable network, or a satellite communication link. Further,the modem may operably communicate with a single user or multiple users.

In an embodiment, a queued burst of traffic is uplink traffic, downlinktraffic, or both uplink traffic and downlink traffic.

In an aspect, a non-transitory computer-readable medium has a pluralityof non-transitory instructions executable with a processor fordetermining an optimal transmission time through a modem, the pluralityof non-transitory instructions being executable for: monitoring atraffic rate through a modem over a period; identifying a burst in thetraffic rate when the traffic rate exceeds a threshold; measuringinter-burst gaps, where the gaps are defined by a minimum time passageand a maximum time passage; determining a mean and a standard deviationof a lognormal distribution of the inter-burst gaps; using the mean andthe standard deviation of the lognormal distribution in amoment-generating function to identify an average time passage valuewhen the risk of a co-occurring burst is minimized; and inserting theaverage time passage value as a mean in the moment-generating functionto back-calculate an optimal transmission time for a queued burst oftraffic.

In an embodiment, the plurality of non-transitory instructions arefurther executable for instructing the modem to transmit the queuedburst of traffic at the optimal transmission time.

In an embodiment, the plurality of non-transitory instructions arefurther executable for periodically updating the optimal transmissiontime by repeating the steps of monitoring, identifying, measuring,determining, using, inserting and instructing.

In an aspect, a system for determining an optimal transmission timethrough a modem comprises a cable modem termination system (CMTS)operably communicating with a modem and a processor configured tomonitor traffic rate through a modem over a period, to identify a burstin the traffic rate when the traffic rate exceeds a threshold, tomeasure inter-burst gaps, where the gaps are defined by a minimum timepassage and a maximum time passage, to determine a mean and a standarddeviation of a lognormal distribution of the inter-burst gaps, to usethe mean and the standard deviation of the lognormal distribution in amoment-generating function to identify an average time passage valuewhen the risk of a co-occurring burst is minimized, and to insert theaverage time passage value as a mean in the moment-generating functionto back-calculate an optimal transmission time for a queued burst oftraffic.

In an embodiment, the processor is further configured to instruct themodem to transmit the queued burst of traffic at the optimaltransmission time.

In an embodiment, the processor is disposed within the cable modemtermination system or externally to the cable modem termination system.

In an embodiment, the processor is further configured to periodicallyupdate the optimal transmission time by repeating the steps ofmonitoring, identifying, measuring, determining, using, inserting andinstructing.

BRIEF DESCRIPTION OF THE DRAWINGS

Illustrative embodiments of the present invention are described indetail below with reference to the attached drawings.

FIG. 1 is a flowchart illustrating steps in a method for determining anoptimal burst transmission time through a modem, according to anembodiment.

FIG. 2A is a block diagram of an exemplary system for performing methodsdescribed herein.

FIG. 2B is a block diagram of an exemplary computing system in which acomputer readable medium provides instructions for performing methodsdescribed herein.

FIG. 3 is a schematic of log 10 traffic in 1 second intervals (sampledevery 10 seconds), according to an embodiment.

FIG. 4 is a probability distribution function of the time in units of 10seconds between bursts with a lognormal fit line, according to anembodiment.

FIG. 5 is a graph of the mean and standard deviation for one modemshowing the optimal time to send a large burst of data, according to anembodiment.

DETAILED DESCRIPTION

In general, the terms and phrases used herein have their art-recognizedmeaning, which can be found by reference to standard texts, journalreferences and contexts known to those skilled in the art. The followingdefinitions are provided to clarify their specific use in the context ofthis description.

As used herein, a “burst” of data is any data transmission above aspecified percentile of the measured traffic rate for a given data set.“Bursty” data refers to a data set exhibiting a plurality of bursts.

As used herein, the term “network” refers generally to any type oftelecommunications or data network including, without limitation, hybridfiber coaxial (HFC) networks, satellite networks, telco networks, anddata networks (including MANs, WANs, LANs, WLANs, internets, andintranets). Such networks or portions thereof may utilize any one ormore different topologies (e.g., ring, bus, star, loop, etc.),transmission media (e.g., wired/RF cable, RF wireless, millimeter wave,optical, etc.) and/or communications or networking protocols (e.g.,SONET, DOCSIS, IEEE Std. 802.3, ATM, X.25, Frame Relay, 3GPP, 3GPP2,LTE/LTE-A, WAP, SIP, UDP, FTP, RTP/RTCP, H.323, etc.).

As used herein, the term “channel” or “communication channel” refers toa physical transmission medium, such as a wire or optical cable, or adesignated non-tangible broadcast medium, such as a wavelength used toconvey an information signal from a sender(s) to a receiver(s). Achannel has a certain capacity for transmitting information, oftenmeasured by its bandwidth in Hz or its data rate in bits per second.

As used herein, “contention” is a media access method used to share abroadcast medium. For example, in a network, two or more nodes may wishto transmit a message across the same wire at the same time, which wouldresult in a collision. To reduce collisions, current contention methodsrequire a user to listen to the network to ensure the channel is free,then wait an amount of time (designated a “contention window”) beforestarting to transmit.

The hub is any system (e.g., a cable modem termination system (CMTS)),device, software, or combination thereof, typically located in a cablecompany's hub site, or “headend”, which is used to provide high speeddata services (i.e., downstream and upstream transmissions), such ascable Internet and Voice over Internet Protocol. The channels aregenerally network bridges and modems that provide bi-directional datacommunication via radio frequency channels on a Hybrid Fiber-Coaxial(HFC) or Radio Frequency over Glass (RFoG). The channels are used todeliver broadband Internet access in the form of cable Internet, takingadvantage of the high bandwidth of a HFC and RFoG network.

The hub is operable to configure the channels to communicate via aspecific protocol (e.g., Data Over Cable Service InterfaceSpecification, or “DOCSIS”) specification. In this regard, the hub isoperable to send control signals that direct the channels to operate ina particular manner with respect to the employed protocol. In anembodiment, the hub is operable to implement an optimal transmissiontime for a burst of data through a modem, e.g., by embedding the optimaltransmission time in a Physical Link Channel (PLC).

FIG. 1 is a flowchart illustrating steps in a method for determining anoptimal burst transmission time through a modem, according to anembodiment. In step 102, a traffic rate through a modem is monitoredover a period. In step 104, a burst in the traffic rate is identifiedwhen the traffic rate exceeds a threshold. In step 106, inter-burst gapsare measured. The gaps are defined by a minimum time passage betweenneighboring bursts and a maximum time passage between neighboringbursts. For example, if two bursts occur in rapid succession (i.e., lessthan the minimum time passage between neighboring bursts), theinter-burst counter restarts after the second burst. In step 108, a meanand a standard deviation of a lognormal distribution of the inter-burstgaps is determined. Then, in step 110, the mean and the standarddeviation of the lognormal distribution are used in a moment-generatingfunction to identify an average time passage value when the risk of aco-occurring burst is minimized. In step 112, the average time passagevalue is inserted as the mean in the moment-generating function toback-calculate an optimal transmission time for a queued burst oftraffic. In step 114, the modem is instructed to transmit the queuedburst of traffic at the optimal transmission time. As shown by thedashed arrow in FIG. 1 , the optimal transmission time is optionallyperiodically updated by repeating the steps of monitoring, identifying,measuring, determining, using, inserting and instructing.

The embodiments herein may be implemented in a variety of ways as amatter of design choice. For example, the invention can take the form ofan entirely hardware embodiment, an entirely software embodiment or anembodiment containing both hardware and software elements.

FIG. 2A is a block diagram of an exemplary system for performing methodsdescribed herein. For example, the system may include a cable modemtermination system (CMTS) 250 configured to transmit/receive datato/from a modem 254 operably communicating with one or more user devices256. The CMTS may, for example, communicate with modem 254 via a cableaccess network that includes a combination of optical fiber and/orcoaxial cables, amplifiers, and electrical/optical converters. Aprocessor 252 is depicted as being disposed within the CMTS, but itshould be recognized that processor 252 may be implemented as a separatedevice from CMTS 250. Processor 252 is configured to monitor trafficrate through a modem over a period, to identify a burst in the trafficrate when the traffic rate exceeds a threshold, to measure inter-burstgaps, where the gaps are defined by a minimum time passage and a maximumtime passage, to determine a mean and a standard deviation of alognormal distribution of the inter-burst gaps, to use the mean and thestandard deviation of the lognormal distribution in a moment-generatingfunction to identify an average time passage value when the risk of aco-occurring burst is minimized, and to insert the average time passagevalue as a mean in the moment-generating function to back-calculate anoptimal transmission time for a queued burst of traffic. CMTS 250 theninstructs modem 254 to transmit the queued burst of traffic at theoptimal transmission time.

In an embodiment, the invention is implemented in software, whichincludes but is not limited to firmware, resident software, microcode,etc. FIG. 2B illustrates a computing system 200 in which a computerreadable medium 206 may provide instructions for performing any of themethods disclosed herein.

Furthermore, the invention can take the form of a computer programproduct accessible from the computer readable medium 206 providingprogram code for use by or in connection with a computer or anyinstruction execution system. For the purposes of this description, thecomputer readable medium 206 can be any apparatus that can tangiblystore the program for use by or in connection with the instructionexecution system, apparatus, or device, including the computer system200.

The medium 206 can be any tangible electronic, magnetic, optical,electromagnetic, infrared, or semiconductor system (or apparatus ordevice). Examples of a computer readable medium 206 include asemiconductor or solid state memory, magnetic tape, a removable computerdiskette, a random access memory (RAM), a read-only memory (ROM), arigid magnetic disk and an optical disk. Some examples of optical disksinclude compact disk-read only memory (CD-ROM), compact disk-read/write(CD-R/W) and DVD.

The computing system 200, suitable for storing and/or executing programcode, can include one or more processors 202 coupled directly orindirectly to memory 208 through a system bus 210. The memory 208 caninclude local memory employed during actual execution of the programcode, bulk storage, and cache memories which provide temporary storageof at least some program code in order to reduce the number of timescode is retrieved from bulk storage during execution. Input/output (1/O)devices 204 (including but not limited to keyboards, displays, pointingdevices, etc.) can be coupled to the system either directly or throughintervening 1/O controllers. Network adapters may also be coupled to thesystem to enable the computing system 200 to become coupled to otherdata processing systems, such as through host systems interfaces 212, orremote printers or storage devices through intervening private or publicnetworks. Modems, cable modem and Ethernet cards are just a few of thecurrently available types of network adapters.

The systems, methods and software disclosed herein are furtherillustrated by the following Example. This Example is for illustrativepurposes only and is not intended to limit the disclosure.

EXAMPLE

This Example discloses a method for optimally sending large amounts ofbursty data through a modem by exploiting the heavy tailed properties ofinter-burst statistics.

The data for this Example were taken from the Mediacom data in spring of2018 consisting of about 31 days worth of data. The data included bothclient and server data for a particular modem. This modem was chosen forhaving fairly high rates of traffic, over 10¹¹ total bytes during theperiod. Additionally, the data were binned in 1-second intervals.

Approach

A “burst” was defined as data above a certain percentile of the trafficrate (bytes) in a time bin (1 second). In the results reported here, thepercentile was defined as the 90th percentile, although other highpercentiles behave similarly. Thus, the time between bursts is the timebetween traffic peaks of this level. This can be seen in FIG. 3 for theparticular device.

Analysis

Fitting and Parameterization

Due to the large scale of the bursts and the associated fitting, it wasnecessary to scale the data by a factor of 10 and then rescale after theanalysis. The results obtained with the device tested are shown in FIG.4 . “Non-collisions” refers to the time between the bursts (defined asin the 90^(th) percentile and above). The curve is the best lognormalfit to the data. Note that the minimum time between bursts was definedto be 10 seconds, meaning that any traffic above the threshold within 10seconds was considered as part of the same burst. Also, consistent withthis definition, the latest spike above the threshold resets the 10second “end of burst” or inter-burst timer to 10 seconds again. Oncethere is a period of 10 seconds from the latest traffic above thethreshold the time from the end of that burst to the next traffic abovethreshold is considered as the time between bursts (inter-burst gap).Thus, the minimum time between bursts was 11 seconds and a maximuminter-burst time was set at 200 seconds. There were a total of 269bursts in the data, as defined this way.

Optimal Time to Send a Burst

Using the average versus the standard deviation of the distribution ofintervals between bursts and exploiting the fact that for a log-normaldistribution it is possible to obtain analytical solutions, one can usethe basic approach described in S. M. Maurer and B. A. Huberman,“Restart strategies and Internet congestion,” Journal of EconomicDynamics and Control, Volume 25, Issues 3-4, March 2001, Pages 641-654.

The curve is constructed using the moment-generating functions for thelognormal. The average time and mean squared average are given in termsof the moments of the distribution by:

${\left\langle t \right\rangle = {\frac{1}{M_{0}}\left\lbrack {M_{1} + {\tau\left( {1 - M_{0}} \right)}} \right\rbrack}}{\left\langle t^{2} \right\rangle = {\frac{1}{M_{0}}\left\lbrack {M_{2} + {{\tau\left( {1 - M_{0}} \right)}\left( {{2\frac{M_{1}}{M_{0}}} + {\tau\left( {\frac{2}{M_{0}} - 1} \right)}} \right)}} \right\rbrack}}$with the n^(th) moment-generating function for the lognormal given by:

${M_{n}(\tau)} = {\frac{1}{2}\exp{\left( {\frac{\sigma^{2}n^{2}}{2} + {\mu n}} \right)\left\lbrack {1 + {{erf}\left( {\frac{{\log\tau} - \mu}{\sigma\sqrt{2}} - \frac{\sigma n}{\sqrt{2}}} \right)}} \right\rbrack}}$so that

$\mu = {{\left\langle t \right\rangle{and}\sigma} = {\sqrt{\left\langle t^{2} \right\rangle - \left\langle t \right\rangle^{2}}.}}$

The resulting <t> versus σ curve is shown in FIG. 5 . The curve is aparametric depiction of the different values of “time to send a burstafter the previous burst,” or time between non-collisions with anotherburst. The optimal transmission time, resides at the cusp of the curve.The interpretation of this optimal transmit time is that it is the besttime to transmit a large amount of data with minimum risk of aco-occurring burst. For the particular set of values described above,the minimum of the curve occurs at an average of 75 seconds. When thisvalue is substituted for M_(n)(τ), the optimal transmit time τ=25.5seconds, which corresponds to the 43^(rd) percentile of the size ofbursts (defined as being between 10 seconds and 200 seconds). That means43% of the bursts will transmit before t, and 43% of the data points inFIG. 4 fall below the corresponding log 10 value of 2.55.

Operationally, τ gives the time that one should wait until transmittinga big burst. The wait time allows for other traffic (e.g., the 43% ofbursts mentioned above) to transmit and clear before time τ, whilewaiting longer increases the likelihood of colliding with a big traffictransmission from another user. Smaller magnitudes of traffic can betransmitted at once.

As the magnitude of a burst threshold is increased, the value of τ willalso increase. For example, at a threshold corresponding to the 92^(nd)percentile, τ=48.2 seconds. This is to be expected, as the largerthreshold means there are fewer bursts so that they will necessarily befarther apart. The relationship between the threshold and τ is alsoexpected to be non-linear because of the heavy tail in the inter-burstgap distribution.

This Example focused on “bursty traffic” to distinguish it from atransmission that is too small to cause capacity problems. For example,the data in this Example used the 90% largest amount of data to define“bursty traffic”, meaning that most of the traffic was less than thatamount by orders of magnitude.

While it may be possible to dispense with the contention window (CW)using this scheme, it may also be possible to incorporate the optimalburst transmission time into a CW scheme. For example, the size of theCW can be set fixed to t and the rest of the algorithm proceeds asbefore. τ should be updated periodically to take into account thenon-stationary nature of the traffic.

STATEMENTS REGARDING INCORPORATION BY REFERENCE AND VARIATIONS

All references cited throughout this application, for example patentdocuments including issued or granted patents or equivalents; patentapplication publications; and non-patent literature documents or othersource material; are hereby incorporated by reference herein in theirentireties, as though individually incorporated by reference, to theextent each reference is at least partially not inconsistent with thedisclosure in this application (for example, a reference that ispartially inconsistent is incorporated by reference except for thepartially inconsistent portion of the reference).

The terms and expressions which have been employed herein are used asterms of description and not of limitation, and there is no intention inthe use of such terms and expressions of excluding any equivalents ofthe features shown and described or portions thereof, but it isrecognized that various modifications are possible within the scope ofthe invention claimed. Thus, it should be understood that although theinvention has been specifically disclosed by preferred embodiments,exemplary embodiments and optional features, modification and variationof the concepts herein disclosed can be resorted to by those skilled inthe art, and that such modifications and variations are considered to bewithin the scope of this invention as defined by the appended claims.The specific embodiments provided herein are examples of usefulembodiments of the invention and it will be apparent to one skilled inthe art that the invention can be carried out using a large number ofvariations of the devices, device components, and method steps set forthin the present description. As will be apparent to one of skill in theart, methods, software and apparatus/devices can include a large numberof optional elements and steps. All art-known functional equivalents ofmaterials and methods are intended to be included in this disclosure.Nothing herein is to be construed as an admission that the invention isnot entitled to antedate such disclosure by virtue of prior invention.

When a group of substituents is disclosed herein, it is understood thatall individual members of that group and all subgroups are disclosedseparately. When a Markush group or other grouping is used herein, allindividual members of the group and all combinations and subcombinationspossible of the group are intended to be individually included in thedisclosure.

It must be noted that as used herein and in the appended claims, thesingular forms “a”, “an”, and “the” include plural reference unless thecontext clearly dictates otherwise. Thus, for example, reference to “aprocessor” includes a plurality of such processors and equivalentsthereof known to those skilled in the art, and so forth. As well, theterms “a” (or “an”), “one or more” and “at least one” can be usedinterchangeably herein. It is also to be noted that the terms“comprising”, “including”, and “having” can be used interchangeably. Theexpression “of any of claims XX-YY” (wherein XX and YY refer to claimnumbers) is intended to provide a multiple dependent claim in thealternative form, and in some embodiments is interchangeable with theexpression “as in any one of claims XX-YY.”

Unless defined otherwise, all technical and scientific terms used hereinhave the same meanings as commonly understood by one of ordinary skillin the art to which this invention belongs. Although any methods andmaterials similar or equivalent to those described herein can be used inthe practice or testing of the present invention, the preferred methodsand materials are described.

Whenever a range is given in the specification, for example, a range ofintegers, a temperature range, a time range, a composition range, orconcentration range, all intermediate ranges and subranges, as well asall individual values included in the ranges given are intended to beincluded in the disclosure. As used herein, ranges specifically includethe values provided as endpoint values of the range. As used herein,ranges specifically include all the integer values of the range. Forexample, a range of 1 to 100 specifically includes the end point valuesof 1 and 100. It will be understood that any subranges or individualvalues in a range or subrange that are included in the descriptionherein can be excluded from the claims herein.

As used herein, “comprising” is synonymous and can be usedinterchangeably with “including,” “containing,” or “characterized by,”and is inclusive or open-ended and does not exclude additional,unrecited elements or method steps. As used herein, “consisting of”excludes any element, step, or ingredient not specified in the claimelement. As used herein, “consisting essentially of” does not excludematerials or steps that do not materially affect the basic and novelcharacteristics of the claim. In each instance herein any of the terms“comprising”, “consisting essentially of” and “consisting of” can bereplaced with either of the other two terms. The inventionillustratively described herein suitably can be practiced in the absenceof any element or elements, limitation or limitations which is/are notspecifically disclosed herein.

What is claimed is:
 1. A method for determining an optimal bursttransmission time comprising: monitoring a traffic rate through acommunication device over a period; identifying bursts in the trafficrate; obtaining burst metrics for a probability distribution of thebursts; using the burst metrics with a moment-generating function forthe probability distribution to determine an optimal transmission timefor a queued burst of traffic when a risk of a co-occurring burst isminimized; and instructing the communication device to transmit thequeued burst of traffic at the optimal transmission time.
 2. The methodof claim 1, wherein the probability distribution is a lognormaldistribution.
 3. The method of claim 1, wherein the burst metricscomprise a mean and a standard deviation.
 4. The method of claim 1,wherein the probability distribution of the bursts comprises inter-burstgap values.
 5. The method of claim 1, wherein the probabilitydistribution of the bursts is a lognormal distribution of inter-burstgap values.
 6. The method of claim 1 further comprising periodicallyupdating the optimal transmission time by repeating the steps ofmonitoring, identifying, obtaining, using, and instructing.
 7. Themethod of claim 1, wherein the optimal transmission time is based on acontinuous timer or wherein the optimal transmission time is a countwithin a contention window.
 8. The method of claim 1, wherein thecommunication device is a single modem, a wireless access point, a 3GPPdefined transceiver, a node in a cable network, an Optical Network Unit(ONU), or a satellite communication link.
 9. The method of claim 1,wherein identifying bursts in the traffic rate comprises noting when thetraffic rate exceeds a threshold.
 10. A non-transitory computer-readablemedium having a plurality of non-transitory instructions executable witha processor for determining an optimal transmission time, the pluralityof non-transitory instructions being executable for: monitoring atraffic rate through a communication device over a period; identifyingbursts in the traffic rate; obtaining burst metrics for a probabilitydistribution of the bursts; using the burst metrics with amoment-generating function for the probability distribution to determinean optimal transmission time for a queued burst of traffic when a riskof a co-occurring burst is minimized; and instructing the communicationdevice to transmit the queued burst of traffic at the optimaltransmission time.
 11. The non-transitory computer-readable medium ofclaim 10 further comprising the plurality of non-transitory instructionsbeing executable for periodically updating the optimal transmission timeby repeating the steps of monitoring, identifying, obtaining, using, andinstructing.
 12. The non-transitory computer-readable medium of claim10, wherein the optimal transmission time is based on a continuous timeror wherein the optimal transmission time is a count within a contentionwindow.
 13. The non-transitory computer-readable medium of claim 10,wherein the communication device is a single modem, a wireless accesspoint, a 3GPP defined transceiver, a node in a cable network, an OpticalNetwork Unit (ONU), or a satellite communication link.
 14. Thenon-transitory computer-readable medium of claim 10, wherein identifyingbursts in the traffic rate comprises noting when the traffic rateexceeds a threshold.
 15. A system for determining an optimaltransmission time through a communication device, comprising: a modemtermination system (MTS) operably communicating with a communicationdevice; and a processor configured to monitor a traffic rate through acommunication device over a period, identify bursts in the traffic rate,obtain burst metrics for a probability distribution of the bursts, usethe metrics with a moment-generating function for the probabilitydistribution to determine an optimal transmission time for a queuedburst of traffic when a risk of a co-occurring burst is minimized, andinstruct the communication device to transmit the queued burst oftraffic at the optimal transmission time.
 16. The system of claim 15,wherein the processor is disposed within the modem termination system orexternally to the modem termination system.
 17. The system of claim 15,wherein the processor is further configured to periodically update theoptimal transmission time by repeating the steps of monitoring,identifying, obtaining, using, and instructing.
 18. The system of claim15, wherein the optimal transmission time is based on a continuous timeror wherein the optimal transmission time is a count within a contentionwindow.
 19. The system of claim 15, wherein the communication device isa single modem, a wireless access point, a 3GPP defined transceiver, anode in a cable network, an Optical Network Unit (ONU), or a satellitecommunication link.
 20. The system of claim 15, wherein identifyingbursts in the traffic rate comprises noting when the traffic rateexceeds a threshold.